> You need to be careful going around labelling people like that just because they made an assumption.

1) Actually, I think you want to be a lot more careful about labelling people as "must be X" because of their gender than about labelling them as "made a sexist comment" because they maybe made a sexist comment. It is actually still worse to be a victim of sexism than to be called a sexist.

2) Having core sexist beliefs isn't a prerequisite for making a sexist comment. You can have a momentary sexist thought without consciously believing that women are inferior to men or anything like that - in fact, momentary sexist thoughts are almost inevitable if you're in a culture where sexism is pervasive, no matter who you are. Moreover, a comment can be sexist even if it is made with completely innocent intentions, if it predictably has the effect of (re)enforcing hierarchical gender roles. Sexism is not an ideology, it's a social structure.

It is actually still worse to be a victim of sexism than to be called a sexist.

Having core sexist beliefs isn't a prerequisite for making a sexist comment.

Exactly, many people think "I'm not a sexist" and then say lots of things, presuming then that everything they say cannot be sexist. I take care to say "sexist talk/action". Tends to get people's backs up less.

You can do "s/sexism/racism/g" for all of the above as well.

Exactly. I've made this same post several times, only doing a bare minimum of s/race/sex/g